Geese, gold, bunnies and the First Law of Thermodynamics

Long before the printing of money, golden eggs were the only currency.

In a deep cave, goose Day-Lewis, the last of the gold-laying geese, was still at work.

Day-Lewis lived in the country known affectionately as Utopia. Every day, Day-Lewis laid 10 perfect golden eggs, and was loved and revered for her service. Luckily, everyone had read Aesop’s fables, and no one tried to kill Day-Lewis to get all those extra eggs out. Still Utopia did pay a few armed guards to keep watch for the illiterates, just in case.

Utopia wasn’t into storing wealth because it wanted to run some important social programs to improve the education and health of the country. Thankfully they didn’t run a deficit and issue bonds so we don’t need to get into any political arguments about libertarianism.

This article is about golden eggs.

Utopia employed the service of bunny Fred to take the golden eggs to the nearby country of Capitalism in return for services of education and health. Every day, bunny Fred took 10 eggs out of the country. Every day, goose Day-Lewis produced 10 eggs. It was a perfect balance. The law of conservation of golden eggs was intact.

Thankfully, history does not record any comment on the value of the services received for these eggs, or on the benefit to society of those services, so we can focus on the eggs story.

Due to external circumstances outside of Utopia’s control, on January 1st, the year of Our Goose 150, a new international boundary was created between Utopia and Capitalism. History does not record the complex machinations behind the reasons for this new border control.

However, as always with government organizations, things never go according to plan. On the first day, January 1st, there were paperwork issues.

Bunny Fred showed up with 10 golden eggs, and, what he thought was the correct paperwork. Nothing got through. Luckily, unlike some government organizations with wafer-thin protections for citizens’ rights, they didn’t practice asset forfeiture for “possible criminal activity we might dream up and until you can prove you earned this honestly we are going to take it and never give it back”. Instead they told Fred to come back tomorrow.

On January 2nd, Bunny Fred had another run at the problem and brought another 10 eggs. The export paperwork for the supply of education and health only allowed for 10 golden eggs to be exported to Capitalism so border control sent on the 10 eggs from Jan 1st and insisted Bunny Fred take 10 eggs take back to Utopia.

On January 3rd, Bunny Fred, desperate to remedy the deficit of services in Utopia took 20 eggs – 10 from Day-Lewis and 10 he had brought back from border control the day before.

Insistent on following their new ad hoc processes, border control could only send on 10 eggs to Capitalism. As they had no approved paperwork for “storing” extra eggs, they insisted that Fred take back the excess eggs.

Every day, the same result:

Day-Lewis produced 10 eggs, Bunny Fred took 20 eggs to border control

Border control sent 10 eggs to Capitalism, Bunny Fred brought 10 eggs back

One day some people who thought they understood the law of conservation of golden eggs took a look at the current situation and declared:

Heretics! This is impossible. Day-Lewis, last of the gold-laying geese, only produces 10 eggs per day. How can Bunny Fred be taking 20 eggs to border control?

You can’t create golden eggs! The law of conservation of golden eggs has been violated.

Share this:

Like this:

Related

21 Responses

If we draw a boundary around the outside of border control we see that 10 golden eggs are created inside every day and 10 golden eggs leave the system.

If we draw a boundary around the inside and outside of border control – i.e., we just isolate border control – we see that 20 golden eggs arrive every day from Utopia, 10 are sent outwards to Capitalism, 10 sent back inwards to Utopia.

If we draw a boundary around Utopia we see that 10 are created inside every day, 10 arrive back in from border control, and 20 are sent out to border control.

Of course, I know for sure that no one is going to say that this example violates the principle of the conservation of golden eggs.

However, in identical parallels (given in the links at the end of the article) many people claim the examples I provide are violating the conservation of energy.

Adding up and subtracting is a technical skill, and it turns out to be much easier doing this with golden eggs than with Joules.

Another fantasy tale to back the first fantasy tale? Yeah! That’s science! LOL!

First, the bunny taking back eggs to Utopia has nothing to do with thermal transfer. For your story to be consistent, the bunny can’t transfer 10 eggs where there is an equal or greater number of eggs. With that principle in mind, 20 eggs can’t be accumulated.

If you really want to impress us, do an experiment. Show us that you can turn 1000W of power into 2000W. Use a Watt meter and take the measurements, videotape it and post it. Also show us by experiment that thermodynamics doesn’t matter. Tb can be the same temperature as Ta and somehow, using bunny magic, Tb can warm up Ta.

The accounting analogy SoD uses is a very good one, as financial accounting depends on “conservation of money” (if you’re not a central bank, that is…). Many technical fields as well use conservation equations for key solutions in completely analogous ways. You cannot solve electrical circuit problems without Kirchhoff’s Current Law, which is conservation of electrical charge.

My old heat transfer textbooks are full of “thermal circuit” diagrams, because the analogies of heat flow to current flow and temperature (or T^4) to voltage are very good.

Here’s another similar experiment. I took a heavily insulated box with a black painted metal bottom and covered it with three layers of material at three inch intervals that transmit solar radiation but not thermal radiation, glass, polycarbonate and acrylic. I attached a thermocouple to each layer and pointed the boxes towards the sun so that the bottom surface was perpendicular to the incoming light. There was also a thermocouple to measure the ambient air temperature This is the plot of the temperature with time. The temperature of the metal plate at the bottom of the box was about 140°C or 413K. That means it was radiating ~1600W/m². Direct normal sunlight at the surface is about 1000W/m². That would correspond to a blackbody temperature of 364K. Some light is reflected at each interface, so the bottom plate is seeing less than 1000W/m². It isn’t 1,000 to 2,000, but it’s not far off.

Now Eli had a talk with Fred, and Fred admitted that to avoid the hassle, after a while he was skimming an egg every few days or so until he got it back down to 10, after which no problems and some very fine carrots came his way.

……….. Eventually Fred realized that taking 20 eggs to the border was a waste of time because they were never going to be let thru. Since Utopia had no use value for the extra 10 eggs Fred came up with a plan. One day he took a detour on the way to the border past Utopia beautiful, deep ocean and he tossed the extra eggs into the sea where they sank to the abyssal depths. No longer did Fred have to carry around the extra eggs and nobody ever had to worry about them never, ever again.
The End

“You are creating energy.. you have created a machine with greater than 100% efficiency.. so I can just tap into this extra energy and have a free source of energy..” – and so on.

But it’s extremely simple as the bunny example shows. You only get to take the “extra energy” away once. There is no free lunch. (Note: this example is only an analogy, analogies are for education, not for proof).

– the reason the inner shell heats up (when an outer shell is added) is because energy can’t get out
– if energy can’t get out then it accumulates
– accumulation of energy shows itself as temperature
– higher temperature bodies radiate more
– if we keep the outer shell in place, the higher radiation from the inner shell is supplied by the “back radiation” from the outer shell

-And if we take the outer shell away, the higher radiation from the inner shell causes it to cool down back to its original temperature.

-If we try and “tap into it” by some other mechanism we just cause the inner shell to cool down.

As Curt says on this topic in another article, problems like these are given in the first few weeks of undergraduate thermodynamics. People who can’t solve the examples fail the course.

However, as countless enthusiastic commenters on this blog have demonstrated, once someone has become firmly convinced that a body with an inner source of energy of 1000W, absorbing external radiation of 1000W, cannot radiate 2000W – there is no hope.

As a fan of crackpot science, this post instantly brings to mind the climateofsophistry.com website, where this viewpoint reigns supreme. (The website name is spot-on; it’s about the only thing in the website that does make sense!)

Turbulent, you are incorrect. There is heat transfer involved in both evaporating water and condensing it into precipitation. If you add heat to the system (CO2 absorbing it is a convenient approach in this case) and the systemN (the atmosphere) reacts by evaporating more water, the heat is still there, but in a different form.

It’s evening in the poverty stricken medieval kingdom of Freedonia and the King of Freedonia is ecstatic, having just acquired and housed in his treasury the fabled Goose That Lays The Golden Eggs. This magical creature sleeps during the night but in daylight lays ten golden eggs each day. Naturally the King thinks this is the end to all his financial problems. Unfortunately the King of the neighbouring country of Tyrannia hears about this and decides he wants in on the action. As Tyrannia is a much larger country with a much larger army, the King of Freedonia is forced to sign a treaty to the effect that 10% of all the golden eggs in his treasury, after rounding down to the nearest whole egg, will be given in tribute to Tyrannia each evening.

So lets see what happens. The 1st day the Goose lays 10 eggs so that evening 1 is given in tribute leaving 9 in the treasury. Next day another 10 eggs are laid so there are 19 and still only 1 given in tribute leaving 18. The following day there are 10 more eggs to give 28, so that evening 2 are given in tribute to leave 26. If you work it out this will go on with the number of eggs accumulating until we get into the nineties. Then each evening 9 will be given in tribute and ten laid the next day so the accumulated eggs will increase by 1 until we reach 100. Then of course ten eggs will be given in tribute each evening and replaced each day so the number of eggs coming into Freedonia exactly equals the number going out, but we’ve somehow got an extra 90 golden eggs in the treasury!

This is very similar to what happens in your model of a spherical shell with an internal power source. At first the outer temperature is too low to emit much thermal radiation and energy accumulates. Then as the temperature rises more and more energy is emitted until it exactly equals that released by the internal power source. But during this process a lot of energy is accumulated in the interior.

And the end of our little story? The King of Freedonia is forced to sell all the golden eggs in the treasury to pay his debts. At first of course there are ninety, but after that there will only be 10 each day. With the treasury empty each evening the tribute falls to zero. Outraged at being deprived of this lucrative source of income, the king of Tyrannia invades Freedonia, hangs its King, and after seizing the Goose for himself lives happily ever after!

“At first the outer temperature is too low to emit much thermal radiation and energy accumulates. Then as the temperature rises more and more energy is emitted until it exactly equals that released by the internal power source.”

@David, I really enjoyed your fairy tale and your description of how temperature rises until it equals that released by the power source.

What the last part of my story shows of course, is that once you start using up that reserve of eggs your rate of use will soon fall to the rate of production.Likewise in SOD’s spherical shell model, once you start tapping into the stored energy you will have an initial power surge greater than the power supply from the internal source. But once the stored energy is used up you will not achieve more power than supplied by the internal source. The 1st Law is never violated.

SOD, as Mike has quickly demonstrated, you won’t assail the dragon’s fortress with this analogy. To the converted what you say is readily analogous, yet to the unconverted it is simply inappropriate.

Here we have two groups, both articulate and competent with abstract thought ( being charitable and putting aside the name-calling ) yet there is a single, simple idea that cannot be transmitted from one to the other. I say simple in the strict technical sense of the term, meaning it inhabits a problem space that can be completely defined with a small number of bits of information, not meaning that one must be thick not to “get it”.

I have spent way too long trying to pare down to bare essentials the stumbling block, and still it eludes me. Although calls are made to the Laws of Thermodynamics I get the distinct feeling that this is a secondary issue, a sort of calling up for reinforcements when the standard is under attack. At it’s heart, I believe we have a phenomenon that is intuitive to one group and anti-intuitive to another.

Intuition is common sense in another form, and most people, quite reasonably, will not abandon common-sense, even for the brief time it takes to flirt with a new idea. Being highly practical, I instinctively push back on any idea that offends my common-sense. It just happens that by accident of birth, I’m one of those that finds the idea of radiative equilibrium crashingly obvious.

These types of problems remind me why in so many schools, thermodynamics is considered a “washout” course, weeding out those without the analytical skills and logical rigor needed to solve even quite basic problems.

In the 1980s, I worked for a Silicon Valley company that had a policy of giving technical grillings to graduating applicants. I was assigned to quiz those from mechanical engineering departments, who would just have completed courses in thermodynamics and heat transfer. I was told to find out if they understood what they had studied at a deep level, and so could apply their knowledge to new situations. I quickly found out that radiative heat transfer is what separated the men from the boys, and so focused on that subject, very successfully. But I was kind of dismayed at the number that I interviewed who really had no clue as to the underlying principles.

In the comment threads at blogs like this, I am continually amazed at the number of ways simple thermodynamic subjects can be gotten wrong. Mike takes the 1st LoT to be conservation of power, constraining magnitudes of power flows.

Many just cannot get the concept of radiative exchange, even though it is no more complicated than getting change back when you purchase something. (“What? The cashier shouldn’t be giving you money when you are buying something from the store!!)

I do understand that the idea that it is counter-intuitive to many that a colder object in the proximity of a (separately powered) warmer object could lead to a higher temperature of the warmer object (compared to when the warmer object is in the proximity of an even colder object), and that this can happen even though heat flow is always from hotter to colder.

What? The cashier shouldn’t be giving you money when you are buying something from the store!!

This is so sweety tweetily nice an analogue. Thanks for chuckles.

In general I think people stumble on FLoT because they intuitively mix total and net energy flows, and then stick to their first impression without realizing they are amateurs who should be careful not to let their chutzpah grow too large.

‘The bearing of this experiment upon the action of planetary atmospheres is obvious … the atmosphere admits of the entrance of the solar heat, but checks its exit; and the result is a tendency to accumulate heat at the surface of the planet (Tyndall, 1859a).’ Tyndall J. 1859. On the transmission of heat of different qualities through gases of different kinds – Proceedings of the Royal Institution 3: 155–158.

Clumsy metaphors notwithstanding – Tyndall provided the experimental basis for the atmospheric greenhouse effect 150 years ago. Science has moved on in the interim however. The following is from the US Academies of Science in 2002 – from doyens of climate science – and can be taken at face value.

‘Recent scientific evidence shows that major and widespread climate changes have occurred with startling speed. For example, roughly half the north Atlantic warming since the last ice age was achieved in only a decade, and it was accompanied by significant climatic changes across most of the globe. Similar events, including local warmings as large as 16°C, occurred repeatedly during the slide into and climb out of the last ice age. Human civilizations arose after those extreme, global ice-age climate jumps. Severe droughts and other regional climate events during the current warm period have shown similar tendencies of abrupt onset and great persistence, often with adverse effects on societies.’ Richard Alley, Jochem Marotzke, William Nordhaus, Jonathon Overpeck, Dorothy Peteet, Raymond Pierrehumbert, Roger Pielke Jr, Thomas Stocker, Lynne Talley, J. Michael Wallace.

It is how the terrestrial climate system actually works – small changes in control variables such as greenhouse gases push the globally resonant system past a threshold at which stage the components start to interact chaotically in multiple and changing negative and positive feedbacks – as tremendous energies cascade through powerful subsystems. Nonequilibrium – rather than equilibrium.

Some of these changes have a regularity within broad limits and the planet responds with a broad regularity in changes of ice, cloud, Atlantic thermohaline circulation and ocean and atmospheric circulation. Abrupt climate change – every 20 or 30 years and as much as 16 degrees C in a decade – provides serious added impetus to mitigation of destabilising pressures in an inherently unstable system.